Moving vertices in a way to preserve their relative position from eachother
It seems I have figure out one way to do it, and that is by using a lattice and a lattice modifier. By adding the lattice modifier to the scene, then selecting the object to modify &gt; shift and select the lattice &gt; ctrl +p &gt; deform by lattice, this added a lattice modifier to the mesh and used the selected lattice object. By manipulating the object, the mesh is then manipulated while the vertex grid remains uniform.
You can see in this gif how this is done and looks like (https://gph.is/g/Z7G7JAP) The gif was too large to upload it here.
Another thing that could be usefull for anyone, would be proportional editing mode for this too.